Show that the equation of the plane normal to the curveF(x,y,z) = 0, G(x, y, z) = 0at the...

Show that the equation of the plane normal to the curve

F(x,y,z) = 0, G(x, y, z) = 0

at the point (x1, y1, z1) can be written in the vector form

dr • grad F × grad G = 0,

and write out the equation in rectangular coordinates. Use the results to find the normal planes to the curves of Problem at the points given.

Problem

b) x2 + y2 + z2 = 9,x2 + y2− 8z2 = 0 at (2, 2, 1);

c) x2 + y2 = 1,x + y + z = 0 at(1, 0, −1);